Hollow turbine blades, in particular gas turbine blades, have, in the region of a transition from the blade airfoil to the platform, a curvature, necessary in terms of loading and casting, on an outer surface, wherein accumulations of material arise locally in this fillet-like transition on account of a rectilinear inner design of the cooling ducts provided in the interior, said accumulations of material being harder to cool by a cooling medium that is able to flow there. Such turbine blades are known for example from U.S. Pat. No. 6,019,579 and from WO 2007/012592, wherein the latter proposes cooling the accumulations of material by providing local cooling-air ducts. Furthermore, the document U.S. Pat. No. 2,861,775 shows a turbine blade produced from bent metal sheets.
A turbine blade having a longer service life is additionally known from EP 1 355 041 A1, wherein the contour of the transition from the blade airfoil to the platform in the blade interior is adapted in order to obtain a blade-airfoil wall thickness, even in the transition region, which corresponds approximately to the wall thickness of the rest of the blade airfoil. In that case, the contour is adapted along the entire, closed periphery, i.e. along the platform. The reduced wall thickness can have a negative effect on the service life of the turbine blade for strength reasons, however, this being undesired.